#14514736

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Fitting

M₁₆ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	(C₂×S₅)⋊C₄
commutator	C₂²×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	C₂×C₄⋊S₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#100
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

340 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 40

Permutation generators:

(1,3,2)(4,5)(6,29,8,26,7,28,9,27)(10,24,12,23,11,25,13,22)(14,33,16,30,15,32,17,31)(18,36,20,35,19,37,21,34);(1,3,2,5,4)(6,32,12,35,7,33,13,34)(8,30,11,36,9,31,10,37)(14,28,20,23,15,29,21,22)(16,26,19,24,17,27,18,25)

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240434);